Problem: Simplify; express your answer in exponential form. Assume $n\neq 0, y\neq 0$. $\dfrac{{(n^{-4})^{5}}}{{(n^{5}y^{-5})^{2}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{-4}}$ to the exponent ${5}$ . Now ${-4 \times 5 = -20}$ , so ${(n^{-4})^{5} = n^{-20}}$ In the denominator, we can use the distributive property of exponents. ${(n^{5}y^{-5})^{2} = (n^{5})^{2}(y^{-5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(n^{-4})^{5}}}{{(n^{5}y^{-5})^{2}}} = \dfrac{{n^{-20}}}{{n^{10}y^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-20}}}{{n^{10}y^{-10}}} = \dfrac{{n^{-20}}}{{n^{10}}} \cdot \dfrac{{1}}{{y^{-10}}} = n^{{-20} - {10}} \cdot y^{- {(-10)}} = n^{-30}y^{10}$.